68 Remarks on the Nomenclature of Achromatic 
considerable thickness from its anterior to its posterior surfaces, 
and that it has, properly speaking, no true optical centre. He gives 
two examples, in one of which a change of 5 • 24 inches in distance 
corresponded to a change of • 0067 inch in calculated focal length ; 
in the other a change of 6' 10 inches in distance corresponded to a 
change of '0029 inch in calculated focal length, the objectives used 
in the experiment being uncorrected |ths, so called. If, however, 
Mr. Cross had used for this purpose lower powers, or had made 
greater variations in the distances employed, he would have found 
much greater discrepancies. For example, by measuring the 
magnifying power first at 25 and then at 50 inches, and deducing 
the value of / by the formula of Mr. Cross, I obtained in two cases 
the following equivalent focal lengths : — For a so-called 1£ inch, 
at 50 inches distance, 1 • 2187 inch; at 25 inches distance, 1 1 2468 
inch; difference, '0271 inch. For a so-called 4th, at 50 inches 
distance, '1982 inch; at 25 inches distance, '1893 inch; difference, 
• 0089 inch. 
Moreover, since the achromatic objectives of different makers 
are constructed on different series of curves, and the component 
lenses placed at different distances apart, it will be found that if 
two achromatic objectives magnify the same at any given distance, 
they will no longer do so if the distance is materially changed. 
Hence I am compelled to agree fully with the observations of 
Mr. Cross* that the nominal focal length assigned to an achromatic 
objective can only serve in any case as “a general appellation 
serving to group together objectives of approximately the same 
magnifying power,” and must conclude, therefore, that the English 
and American nomenclature possesses no real claim to strict scientific 
accuracy, and especially that the comparison made by some with 
the case of the celestial telescope is not valid. 
But besides the inevitable inaccuracy resulting from this source, 
there are in the case of the higher powers of modern makers two 
other sources of much more considerable error. The first of these 
involves the case of all those objectives which are provided with a 
screw-collar to correct for thickness of cover ; the second involves 
the case of objectives with two fronts, one for wet and the other for 
dry, or those with but one front which can be used wet or dry by 
merely changing the correction given by the screw-collar. 
The correction for thickness of cover is made, as is well known, 
by changing the distance between the front combination of the 
triplet and the posterior two combinations. As a consequence, the 
magnifying power of the objective at any given distance, or with 
any given eye-piece, is least when the objective is corrected for 
uncovered, and greatest when it is corrected for the thickest cover 
through which it will work. The ratio of this change is very 
* Loc. cit., p. 401. 
